Well at the risk of being hammered since my opinion is on the unpopular side in this thread, I agree with many points here but I will weigh in with my own experience of how wonderful it is when 2 rabbits are raised together colony style. They do really enjoy the companionship - hanging out together, grooming each other, raising babies together. I am really happy they get along so well.
I wouldn't be having this experience though if I hadn't read on this forum that the does will FIGHT LIKE CRAZY and DO NOT SEPARATE THEM or otherwise try to rescue them - a couple days of pulling fur and boxing and the does figured out who's dominant and they've been just sweet and happy ever since. It was worth nervously waiting in the sidelines for a couple days. There was no bloodshed, I would have stopped that.
NOTE that I introduced young does, not full grown adults who are used to their own space. I introduced a 5 month old and a 9 week old. The 5 month old had been with her sister, until her sis died, and got so depressed I went out and got another doe. It did the trick, perked her right back up.
I think it comes down to:
1) How socialized the rabbits are = were they kept with other rabbits or allowed to live in isolation?
2) how old
3) how big is your cage
My does got along even in a smaller cage but that might be an exception. Now they have a huge colony pen and even with 2 tiers of litters in there for a total of some 30 rabbits they are all getting a long just fantastic! Its like a bunny love den in there I love going in there to hang out with all the nudging fluffy rabbits!
My buck on the other hand is over a year old and I think he may be to much of a bully to house with another buck at this point. I may try with one of his offspring - since he's very acquainted with them - they squeeze through the day pen bars. He seems to know they are his, even chased off the cats a few times!
I think House Rabbit Society people are dealing with neutered animals which removes the hormonal & breeding factor- and companionship very much probably depends on the animal. Just as it does with cats - some prefer company, some do not. I don't think we can make a blanket statement about it. For instance I have 4 cats, any one of them would be very lonely by itself. But my previous cat was rather glad when he lost his companion and became the sole cat in the household - he wanted all my attention. I do not know but imagine rabbits might be similar, but I am not sure if they are as complex as all that. I am still figuring that part out. I have a couple of rabbits who seem to like a lot of affection!